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Long Bai

Publications and source records attributed to Long Bai.

126 records · Page 7Linked to original sources
arXiv2022

What is Event Knowledge Graph: A Survey

Besides entity-centric knowledge, usually organized as Knowledge Graph (KG), events are also an essential kind of knowledge in the world, which trigger the spring up of event-centric knowledge representation form like Event KG (EKG). It plays an increasingly important role in many downstream applications, such as search, question-answering, recommendation, financial quantitative investments, and text generation. This paper provides a comprehensive survey of EKG from history, ontology, instance, and application views. Specifically, to characterize EKG thoroughly, we focus on its history, definition, schema induction, acquisition, related representative graphs/systems, and applications. The development processes and trends are studied therein. We further summarize prospective directions to facilitate future research on EKG.

cs.LG↗
arXiv2022

Complex Evolutional Pattern Learning for Temporal Knowledge Graph Reasoning

A Temporal Knowledge Graph (TKG) is a sequence of KGs corresponding to different timestamps. TKG reasoning aims to predict potential facts in the future given the historical KG sequences. One key of this task is to mine and understand evolutional patterns of facts from these sequences. The evolutional patterns are complex in two aspects, length-diversity and time-variability. Existing models for TKG reasoning focus on modeling fact sequences of a fixed length, which cannot discover complex evolutional patterns that vary in length. Furthermore, these models are all trained offline, which cannot well adapt to the changes of evolutional patterns from then on. Thus, we propose a new model, called Complex Evolutional Network (CEN), which uses a length-aware Convolutional Neural Network (CNN) to handle evolutional patterns of different lengths via an easy-to-difficult curriculum learning strategy. Besides, we propose to learn the model under the online setting so that it can adapt to the changes of evolutional patterns over time. Extensive experiments demonstrate that CEN obtains substantial performance improvement under both the traditional offline and the proposed online settings.

cs.AI↗
arXiv2021

Extremes of Gaussian random fields with non-additive dependence structure

We derive exact asymptotics of $$\mathbb{P}\left(\sup_{\mathbf{t}\in {\mathcal{A}}}X(\mathbf{t})>u\right),~ \text{as}~ u\to\infty,$$ for a centered Gaussian field $X(\mathbf{t}),~ \mathbf{t}\in \mathcal{A}\subset\mathbb{R}^n$, $n>1$ with continuous sample paths a.s., for which $\arg \max_{\mathbf{t}\in {\mathcal{A}}} Var(X(\mathbf{t}))$ is a Jordan set with finite and positive Lebesque measure of dimension $k\leq n$ and its dependence structure is not necessarily locally stationary. Our findings are applied to deriving the asymptotics of tail probabilities related to performance tables and chi processes where the covariance structure is not locally stationary.

math.PR↗
arXiv2021

Integrating Deep Event-Level and Script-Level Information for Script Event Prediction

Scripts are structured sequences of events together with the participants, which are extracted from the texts.Script event prediction aims to predict the subsequent event given the historical events in the script. Two kinds of information facilitate this task, namely, the event-level information and the script-level information. At the event level, existing studies view an event as a verb with its participants, while neglecting other useful properties, such as the state of the participants. At the script level, most existing studies only consider a single event sequence corresponding to one common protagonist. In this paper, we propose a Transformer-based model, called MCPredictor, which integrates deep event-level and script-level information for script event prediction. At the event level, MCPredictor utilizes the rich information in the text to obtain more comprehensive event semantic representations. At the script-level, it considers multiple event sequences corresponding to different participants of the subsequent event. The experimental results on the widely-used New York Times corpus demonstrate the effectiveness and superiority of the proposed model.

cs.CL↗
arXiv2021

The Influence of Age and Gender Information on the Diagnosis of Diabetic Retinopathy: Based on Neural Networks

This paper proposes the importance of age and gender information in the diagnosis of diabetic retinopathy. We utilized Deep Residual Neural Networks (ResNet) and Densely Connected Convolutional Networks (DenseNet), which are proven effective on image classification problems and the diagnosis of diabetic retinopathy using the retinal fundus images. We used the ensemble of several classical networks and decentralized the training so that the network was simple and avoided overfitting. To observe whether the age and gender information could help enhance the performance, we added the information before the dense layer and compared the results with the results that did not add age and gender information. We found that the test accuracy of the network with age and gender information was 2.67% higher than that of the network without age and gender information. Meanwhile, compared with gender information, age information had a better help for the results.

eess.IV↗
arXiv2019

On generalized Piterbarg-Berman function

This paper aims to evaluate the Piterbarg-Berman function given by $$\mathcal{P\!B}_α^h(x, E) = \int_\mathbb{R}e^z\mathbb{P} \left\{{\int_E \mathbb{I}\left(\sqrt2B_α(t) - |t|^α- h(t) - z>0 \right) {\text{d}} t > x} \right\} {\text{d}} z,\quad x\in[0, {mes}(E)],$$ with $h$ a drift function and $B_α$ a fractional Brownian motion (fBm) with Hurst index $α/2\in(0,1]$, i.e., a mean zero Gaussian process with continuous sample paths and covariance function \begin{align*} {\mathrm{Cov}}(B_α(s), B_α(t)) = \frac12 (|s|^α+ |t|^α- |s-t|^α). \end{align*} This note specifies its explicit expression for the fBms with $α=1$ and $2$ when the drift function $h(t)=ct^α, c>0$ and $E=\mathbb{R}_+\cup\{0\}$. For the Gaussian distribution $B_2$, we investigate $\mathcal{P\!B}_2^h(x, E)$ with general drift functions $h(t)$ such that $h(t)+t^2$ being convex or concave, and finite interval $E=[a,b]$. Typical examples of $\mathcal{P\!B}_2^h(x, E)$ with $h(t)=c|t|^λ-t^2$ and several bounds of $\mathcal{P\!B}_α^h(x, E)$ are discussed. Numerical studies are carried out to illustrate all the findings. Keywords: Piterbarg-Berman function; sojourn time; fractional Brownian motion; drift function

math.ST↗
arXiv2019

Extremes of multifractional Brownian motion

Let $B_{H}(t), t\geq [0,T], T\in(0,\infty)$ be the standard Multifractional Brownian Motion(mBm), in this contribution we are concerned with the exact asymptotics of \begin{eqnarray*} \mathbb{P}\left\{\sup_{t\in[0,T]}B_{H}(t)>u\right\} \end{eqnarray*} as $u\rightarrow\infty$. Mainly depended on the structures of $H(t)$, the results under several important cases are investigated.

math.PR↗
arXiv2018

Extremes of Locally-stationary Chi-square processes on discrete grids

For $X_i(t), i=1,\ldots, n, t\in [0,T]$ centered Gaussian processes, the chi-square process $\sum_{i=1}^{n}X_i^2(t)$ appears naturally as limiting processes in various statistical models. In this paper, we are concerned with the exact tail asymptotics of the supremum taken over discrete grids of a class of locally stationary chi-square processes where $X_i(t),\ 1\leq i\leq n$ are not identical. An important tool for establishing our results is a generalisation of Pickands lemma under the discrete scenario. An application related to the change-point problem is discussed.

math.PR↗
arXiv2018

Extremes of Gaussian chaos processes with Trend

Let $\boldsymbol{X}(t)=(X_1(t),\ldots,X_d(t)), t\in [0,S]$ be a Gaussian vector process and let $g(\boldsymbol{x}),\boldsymbol{x}\in\mathbb{R}^d$ be a continuous homogeneous function. In this paper we are concerned with the exact tail asymptotics of the chaos process $g(\boldsymbol{X}(t))+ h(t),t\in [0,S]$ with trend function $h$. Both scenarios $\boldsymbol{X}(t)$ is locally-stationary and $\boldsymbol{X}(t)$ is non-stationary are considered. Important examples include the product of Gaussian processes and chi-processes.

math.PR↗
arXiv2018

Ruin problem for Brownian motion risk model with interest rate and tax payment

Let $\{B(t), t\ge 0\}$ be a Brownian motion. Consider the Brownian motion risk model with interest rate collection and tax payment defined by \begin{align}\label{Rudef} \widetilde{U}_γ^δ(t)=\widetilde{X}^δ(t)-γ\sup_{s\in[0,t]} \left(\widetilde{X}^δ(s)e^{δ(t-s)}-ue^{δ(t-s)}\right),t\ge0, \end{align} with $$\widetilde{X}^δ(t)=ue^{δt}+c \int_0^t e^{δ(t-v)}dv-σ\int_0^t e^{δ(t-v)}dB(v),$$ where $c>0,γ\in [0,1)$ and $δ\in \mathbb{R}$ are three given constants. When $δ=0$ and $γ\in (0,1)$ this is the risk model introduced from Albrecher and Hipp in \cite{AH2007} where the ruin probability in the infinite time horizon has been explicitly calculated. In the presence of interest rate $δ\neq0$, the calculation of ruin probability for this risk process for both finite and infinite time horizon seems impossible. In the paper, based on asymptotic theory we propose an approximation for ruin probability and ruin time when the initial capital $u$ tends to infinity. Our results are of interest given the fact that this can be used as benchmark model in various calculations.

math.PR↗
arXiv2018

Extremes of $L^p$-norm of Vector-valued Gaussian processes with Trend

Let $\boldsymbol{X}(t)=(X_1(t),\ldots,X_d(t))$ be a Gaussian vector process and $g(t)$ be a continuous function. The asymptotics of distribution of $\left\|\boldsymbol{X}(t)\right\|_p$, the $L^p$ norm for Gaussian finite-dimensional vector, have been investigated in numerous literatures. In this contribution we are concerned with the exact tail asymptotics of $\left\|\boldsymbol{X}(t)\right\|^c_p,\ c>0, $ with trend $g(t)$ over $[0,T]$. Both scenarios that $\boldsymbol{X}(t)$ is locally stationary and non-stationary are considered. Important examples include $\sum_{i=1}^d \left|X_i(t)\right|+g(t)$ and chi-square processes with trend, i.e., $\sum_{i=1}^d X_i^2(t)+g(t)$. These results are of interest in applications in engineering, insurance and statistics, etc.

math.PR↗
arXiv2018

Estimation of Change-point Models

We consider the testing and estimation of change-points, locations where the distribution abruptly changes, in a sequence of observations. Motivated by this problem, in this contribution we first investigate the extremes of Gaussian fields with trend which then help us give asymptotic p-value approximations of the likelihood ratio statistics from change-point models.

math.PR↗
arXiv2018

Approximation of Kolmogorov-Smirnov Test Statistics

Motivated by the weak limit of the Kolmogorov-Smirnov test statistics, in this contribution, we concern the asymptotics of \begin{align*} \mathbb{P}\left\{\sup_{\boldsymbol{x}\in [0,1]^n}\left(W(\boldsymbol{x})\Big| W(\boldsymbol{1})=w\right)>u\right\}, \ w\in\mathbb{R}, \end{align*} for large $u$ where $W(\boldsymbol{x})$ is the multivariate Brownian sheet based on a distribution function $F$. The results related to general $F$ are investigated and some important examples are also showed.

math.PR↗
arXiv2018

Drawdown and drawup for fractional Brownian motion with trend

In this paper, we consider the drawdown and drawup of the fractional Brownian motion with trend, which corresponds to the logarithm of geometric fractional Brownian motion representing the stock price in financial market. We derive the asymptotics of tail probabilities of the maximum drawdown and maximum drawup as the threshold goes to infinity, respectively. It turns out that the extremes of drawdown leads to new scenarios of asymptotics depending on Hurst index of fractional Brownian motion.

math.PR↗
arXiv2018

Extremes of vector-valued Gaussian processes with Trend

Let $X(t)=(X_1(t), \dots, X_n(t)), t\in \mathcal{T}\subset \mathbb{R} $ be a centered vector-valued Gaussian process with independent components and continuous trajectories, and $h(t)=(h_1(t),\dots, h_n(t)), t\in \mathcal{T} $ be a vector-valued continuous function. We investigate the asymptotics of $$\mathbb{P}\left(\sup_{t\in \mathcal{T} } \min_{1\leq i\leq n}(X_i(t)+h_i(t))>u\right)$$ as $u\to\infty$. As an illustration to the derived results we analyze two important classes of $X(t)$: with locally-stationary structure and with varying variances of the coordinates, and calculate exact asymptotics of simultaneous ruin probability and ruin time in a Gaussian risk model.

math.PR↗
arXiv2017

Parisian ruin of Brownian motion risk model over an infinite-time horizon

Let $B(t), t\in \mathbb{R}$ be a standard Brownian motion. In this paper, we derive the exact asymptotics of the probability of Parisian ruin on infinite time horizon for the following risk process \begin{align}\label{Rudef} R_u^δ(t)=e^{δt}\left(u+c\int^{t}_{0}e^{-δv}d v-σ\int_{0}^{t}e^{-δv}d B(v)\right),\quad t\geq0, \end{align} where $u\geq 0$ is the initial reserve, $δ\geq0$ is the force of interest, $c>0$ is the rate of premium and $σ>0$ is a volatility factor. Further, we show the asymptotics of the Parisian ruin time of this risk process.

math.PR↗
arXiv2016

Parisian Ruin of the Brownian Motion Risk Model with Constant Force of Interest

Let $B(t), t\in \mathbb{R}$ be a standard Brownian motion. Define a risk process \label{Rudef} R_u^δ(t)=e^{δt}\left(u+c\int^{t}_{0}e^{-δs}d s-σ\int_{0}^{t}e^{-δs}d B(s)\right), t\geq0, where $u\geq 0$ is the initial reserve, $δ\geq0$ is the force of interest, $c>0$ is the rate of premium and $σ>0$ is a volatility factor. In this contribution we obtain an approximation of the Parisian ruin probability \mathcal{K}_S^δ(u,T_u):=\mathbb{P}\left\{\inf_{t\in[0,S]} \sup_{s\in[t,t+T_u]} R_u^δ(s)<0\right\}, S\ge 0, as $u\rightarrow\infty$ where $T_u$ is a bounded function. Further, we show that the Parisian ruin time of this risk process can be approximated by an exponential random variable. Our results are new even for the classical ruin probability and ruin time which correspond to $T_u\equiv0$ in the Parisian setting.

math.PR↗